Rational Linkages Toolbox Documentation

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Welcome to the Rational Linkages Toolbox Documentation, which serves as a reference for the toolbox. The toolbox is a collection of functions for the analysis of rational linkages and their rapid prototyping. It is written in Python and uses the Numpy and SymPy libraries for computations, and Matplotlib for plotting. The toolbox is developed at the Unit of Geometry and Surveying, University of Innsbruck, Austria.

The source code is available as Gitlab repository hosted by UIBK. The installation instructions can be found in the installation manual.

Since the self-hosted repository does not allow external users to create issues, please, use the external issue tracker hosted on Github for submitting issues and feature requests.

Run live examples of the toolbox in your browser using the Binder service. Click on the badge below to start the Binder session:


In case of other questions or contributions, please, email the author at: daniel.huczala@uibk.ac.at

Indices and tables


The toolbox is developed by the Unit of Geometry and Surveying, University of Innsbruck, Austria. Namely, the following people contributed to the development and writing documentation:

  • Daniel Huczala (author, maintainer)

  • Daren A. Thimm (contributor)

  • Martin Pfurner (contributor)

  • Hans-Peter Schröcker (supervisor, contributor)

Citing the Package

If you use the Rational Linkages Toolbox in your research, please, cite it as follows:

Huczala, D., Siegele J., Thimm, D., Pfurner, M., Schröcker, H.-P. (2024). Rational Linkages: From Poses to 3D-printed Prototypes. Advances in Robot Kinematics 2024. ARK 2024. Preprint arXiv:2403.00558, url: https://arxiv.org/abs/2403.00558.

   title={Rational Linkages: From Poses to 3D-printed Prototypes},
   author={Daniel Huczala and Johannes Siegele and Daren A. Thimm and Martin Pfurner and Hans-Peter Schröcker},
   booktitle="Advances in Robot Kinematics 2024, ARK 2024",


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Funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or the European Research Executive Agency (REA). Neither the European Union nor the granting authority can be held responsible for them.

We would like to thank our colleagues outside the Unit of Geometry and Surveying, who contributed to the development of the toolbox and helped with implementation of their algorithms and suggestions. These people are namely:

  • Johannes Gerstmayr, University of Innsbruck, Austria, for the help with creating the interface to his Exudyn [1] software. More on this in section Dynamics Simulations - Exudyn Integration.

  • Georg Nawratil, Technical University of Vienna, Austria,

  • and Zijia Li, Chinese Academy of Sciences, China, for their help with the implementation of the Combinatorial Search Algorithm of collision-free linkages [2]. More on this in section Combinatorial Optimization.

  • Johannes Siegele, Austrian Academy of Sciences, Austria, for his help with the implementation of the algorithm for motion interpolation of 4 poses. More on this in section Cubic Interpolation of Four Poses.